Published 2021-12-14
Keywords
- Coreflective subcategory; Coreflective hull; Hereditary coreflective subcategory.
Abstract
In this paper, first we show that the category of discrete fuzzy topological spaces, the category of those fuzzy topological spaces, in which open fuzzy sets are closed and the category of those fuzzy topological spaces, which can be written as the disjoint union of discrete or indiscrete fuzzy topological spaces, are proper hereditary coreflective subcategories of the category MC-FTS of meet-complete fuzzy topological spaces. We also show that the coreflective hull of an object of MC-FTS need not coincide with its hereditary coreflective hull. It is shown that the coreflective subcategories of the category FTS of fuzzy topological spaces, which are subcategories of the category MC-FTS need not be hereditary. We also show that if a fuzzy topological space is not meet-complete, then its coreflective hull does not contain MC-FTS.